ICT Integration: Why use Google Earth?
Why ICT?
It is increasingly important for students to gain exposure to computer use as part of their mathematics education. This statement is reflected in the Board of Senior Secondary Studies (2009) unit outline, which states that “Technology, its selection and appropriate use, is an integral part” of students mathematical achievement, and that “computational fluency” is an essential skill inherent in mathematics. Further, evidence suggests that students who regularly use computers in an educational content have better assessment outcomes (O’Dwyer et al. 2008)
In mathematics education, technology has long played a role (in terms of calculators and spread sheets) however, as the wealth offered by ICT swells, so must its incorporation into mathematics lessons increase. Goos et al. (2003) have proposed a model for ICT integration into mathematics education in terms of a series of metaphors of student and teacher relationships with technology. Namely,
Technology as;
- master
- occurs when users have only a limited limited abilities with the technology
- students may not lack mathematical understanding to make sense of computer generated content or output
- servant
- technology as an efficiency tool.
- replaces pen and paper calculations but doesn’t change the nature of the task
- partner
- creative uses of technology provide new kinds of tasks or new ways of approaching existing tasks
- allows exploration of different perspectives and allows deeper understanding
- an extension of self
- freedom afforded by an expert command of technologies
- permeates all facets of pedagogy and student learning approaches
I believe that this task represents a partnership with technology. The reformulation of the task to the Google Earth environment is not merely cosmetic but further, allows a new way of engaging with the problem and the course content. Although the task is structured, it allows some open exploration which will afford a deeper understanding of the mathematical concepts and their application.
Why Google Earth?
Google Earth is gaining recognition as an educational tool (see for example RealWorldMath.org, Google Earth Lessons, or Designing and Creating Earth Science Lessons with Google Earth^{TM}) and rightly so. The combination of an enormous dataset combined with an easily navigable visualisation environment, has made Google Earth a popular option for science and geography teachers wanting to integrate ICT into their lessons. Increasingly, mathematics teachers are using Google Earth’s built in ruler and protractor as tools to engage students in their learning of topics such as mensuration, coordinate geometry, plane geometry and trigonometry. I was however, surprised that I was unable to find any mention of lessons using Google Earth in a ‘shadow reckoning’ task such as the one described here.
The ruler tool allows students to quickly measure the length and true bearing of real world objects from their photos captured in Google Earth objects. Using the Google Earth ruler is valuable in itself as it provides experience using yet another tool for measurement, but further it models conventions of measurement such as units and significant figures. The opportunity for learning from the instant feedback given by computer-based tools such as this is noted by Goos, Stillman and Vale (2007)
The constant necessity for zooming in and out also gives students exposure to concrete examples of scaling and similar figures
The range of visualisation tools provides opportunities for students to view the problem from a number of perspectives and affords exploration and reformulation of the question into a form which is more intuitive for them.
An example is the inclusion of 3D buildings with Google Earth. This provides students the option of seeing the problem as it conventionally presented in terms of a horizontal view. Note, I have overlayed the ghosted-yellow right-triangle as a representation of the geometric visualisation that must occur in students’ minds such that they can formulate an approach to the problem. This direct visualisation aid is not available to students in contrast to the traditional formulation of this question as discussed in another post.
Board of Senior Secondary Studies (BSSS). (2009). Mathematical Applications unit outline. Retrieved from the BSSS website: http://www.bsss.act.edu.au/__data/assets/word_doc/0019/123319/Mathematical_Applications_T_0812_v2.doc
Goos, M., Galbraith, P., Renshaw, P. & Geiger, V. (2003). Perspectives on technology mediated learning in secondary school mathematics classrooms. Journal of Mathematical Behavior, 22, 73-89
Goos, M., Stillman, G. & Vale, C. (2007). Teaching secondary mathematics: Research and practice for the 21st century. Crows Nest, Australia: Allen & Unwin.
O’Dwyer,L,.M., Russell,M., Bebell,D. & Seeley,K. (2008). Examining the Relationship between Students’ MathematicsTest Scores and Computer Use at Home and at School. The Journal of Technology, Learning, and Assessment. 6, 5, pp. 1-45.
Hee hee! Funny banner pic! Lovely analysis using Goos. I think you’ve correctly identified where your task sits.